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<div class="subTitle">org.apache.commons.math3.analysis.polynomials</div>
<h2 title="Class PolynomialFunctionNewtonForm" class="title">Class PolynomialFunctionNewtonForm</h2>
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<dt>All Implemented Interfaces:</dt>
<dd><a href="../../../../../../org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.html" title="interface in org.apache.commons.math3.analysis.differentiation">UnivariateDifferentiableFunction</a>, <a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></dd>
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<pre>public class <span class="strong">PolynomialFunctionNewtonForm</span>
extends <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a>
implements <a href="../../../../../../org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.html" title="interface in org.apache.commons.math3.analysis.differentiation">UnivariateDifferentiableFunction</a></pre>
<div class="block">Implements the representation of a real polynomial function in
 Newton Form. For reference, see <b>Elementary Numerical Analysis</b>,
 ISBN 0070124477, chapter 2.
 <p>
 The formula of polynomial in Newton form is
     p(x) = a[0] + a[1](x-c[0]) + a[2](x-c[0])(x-c[1]) + ... +
            a[n](x-c[0])(x-c[1])...(x-c[n-1])
 Note that the length of a[] is one more than the length of c[]</p></div>
<dl><dt><span class="strong">Since:</span></dt>
  <dd>1.2</dd></dl>
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<th class="colOne" scope="col">Constructor and Description</th>
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<td class="colOne"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#PolynomialFunctionNewtonForm(double[],%20double[])">PolynomialFunctionNewtonForm</a></strong>(double[]&nbsp;a,
                            double[]&nbsp;c)</code>
<div class="block">Construct a Newton polynomial with the given a[] and c[].</div>
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<th class="colLast" scope="col">Method and Description</th>
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<td class="colFirst"><code>protected void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#computeCoefficients()">computeCoefficients</a></strong>()</code>
<div class="block">Calculate the normal polynomial coefficients given the Newton form.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>int</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#degree()">degree</a></strong>()</code>
<div class="block">Returns the degree of the polynomial.</div>
</td>
</tr>
<tr class="altColor">
<td class="colFirst"><code>static double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#evaluate(double[],%20double[],%20double)">evaluate</a></strong>(double[]&nbsp;a,
        double[]&nbsp;c,
        double&nbsp;z)</code>
<div class="block">Evaluate the Newton polynomial using nested multiplication.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#getCenters()">getCenters</a></strong>()</code>
<div class="block">Returns a copy of the centers array.</div>
</td>
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<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#getCoefficients()">getCoefficients</a></strong>()</code>
<div class="block">Returns a copy of the coefficients array.</div>
</td>
</tr>
<tr class="rowColor">
<td class="colFirst"><code>double[]</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#getNewtonCoefficients()">getNewtonCoefficients</a></strong>()</code>
<div class="block">Returns a copy of coefficients in Newton form formula.</div>
</td>
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<tr class="altColor">
<td class="colFirst"><code><a href="../../../../../../org/apache/commons/math3/analysis/differentiation/DerivativeStructure.html" title="class in org.apache.commons.math3.analysis.differentiation">DerivativeStructure</a></code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#value(org.apache.commons.math3.analysis.differentiation.DerivativeStructure)">value</a></strong>(<a href="../../../../../../org/apache/commons/math3/analysis/differentiation/DerivativeStructure.html" title="class in org.apache.commons.math3.analysis.differentiation">DerivativeStructure</a>&nbsp;t)</code>
<div class="block">Simple mathematical function.</div>
</td>
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<tr class="rowColor">
<td class="colFirst"><code>double</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#value(double)">value</a></strong>(double&nbsp;z)</code>
<div class="block">Calculate the function value at the given point.</div>
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<tr class="altColor">
<td class="colFirst"><code>protected static void</code></td>
<td class="colLast"><code><strong><a href="../../../../../../org/apache/commons/math3/analysis/polynomials/PolynomialFunctionNewtonForm.html#verifyInputArray(double[],%20double[])">verifyInputArray</a></strong>(double[]&nbsp;a,
                double[]&nbsp;c)</code>
<div class="block">Verifies that the input arrays are valid.</div>
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<h3>Methods inherited from class&nbsp;java.lang.<a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</a>, <a href="http://docs.oracle.com/javase/7/docs/api/java/lang/Object.html?is-external=true#wait(long,%20int)" title="class or interface in java.lang">wait</a></code></li>
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<h4>PolynomialFunctionNewtonForm</h4>
<pre>public&nbsp;PolynomialFunctionNewtonForm(double[]&nbsp;a,
                            double[]&nbsp;c)
                             throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
                                    <a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
                                    <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre>
<div class="block">Construct a Newton polynomial with the given a[] and c[]. The order of
 centers are important in that if c[] shuffle, then values of a[] would
 completely change, not just a permutation of old a[].
 <p>
 The constructor makes copy of the input arrays and assigns them.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - Coefficients in Newton form formula.</dd><dd><code>c</code> - Centers.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if any argument is <code>null</code>.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if any array has zero length.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the size difference between
 <code>a</code> and <code>c</code> is not equal to 1.</dd></dl>
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<h4>value</h4>
<pre>public&nbsp;double&nbsp;value(double&nbsp;z)</pre>
<div class="block">Calculate the function value at the given point.</div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html#value(double)">value</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../org/apache/commons/math3/analysis/UnivariateFunction.html" title="interface in org.apache.commons.math3.analysis">UnivariateFunction</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>z</code> - Point at which the function value is to be computed.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the function value.</dd></dl>
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<h4>value</h4>
<pre>public&nbsp;<a href="../../../../../../org/apache/commons/math3/analysis/differentiation/DerivativeStructure.html" title="class in org.apache.commons.math3.analysis.differentiation">DerivativeStructure</a>&nbsp;value(<a href="../../../../../../org/apache/commons/math3/analysis/differentiation/DerivativeStructure.html" title="class in org.apache.commons.math3.analysis.differentiation">DerivativeStructure</a>&nbsp;t)</pre>
<div class="block">Simple mathematical function.
 <p><a href="../../../../../../org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.html" title="interface in org.apache.commons.math3.analysis.differentiation"><code>UnivariateDifferentiableFunction</code></a> classes compute both the
 value and the first derivative of the function.</p></div>
<dl>
<dt><strong>Specified by:</strong></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.html#value(org.apache.commons.math3.analysis.differentiation.DerivativeStructure)">value</a></code>&nbsp;in interface&nbsp;<code><a href="../../../../../../org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.html" title="interface in org.apache.commons.math3.analysis.differentiation">UnivariateDifferentiableFunction</a></code></dd>
<dt><span class="strong">Parameters:</span></dt><dd><code>t</code> - function input value</dd>
<dt><span class="strong">Returns:</span></dt><dd>function result</dd><dt><span class="strong">Since:</span></dt>
  <dd>3.1</dd></dl>
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<h4>degree</h4>
<pre>public&nbsp;int&nbsp;degree()</pre>
<div class="block">Returns the degree of the polynomial.</div>
<dl><dt><span class="strong">Returns:</span></dt><dd>the degree of the polynomial</dd></dl>
</li>
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<a name="getNewtonCoefficients()">
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<h4>getNewtonCoefficients</h4>
<pre>public&nbsp;double[]&nbsp;getNewtonCoefficients()</pre>
<div class="block">Returns a copy of coefficients in Newton form formula.
 <p>
 Changes made to the returned copy will not affect the polynomial.</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a fresh copy of coefficients in Newton form formula</dd></dl>
</li>
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<h4>getCenters</h4>
<pre>public&nbsp;double[]&nbsp;getCenters()</pre>
<div class="block">Returns a copy of the centers array.
 <p>
 Changes made to the returned copy will not affect the polynomial.</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a fresh copy of the centers array.</dd></dl>
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<h4>getCoefficients</h4>
<pre>public&nbsp;double[]&nbsp;getCoefficients()</pre>
<div class="block">Returns a copy of the coefficients array.
 <p>
 Changes made to the returned copy will not affect the polynomial.</p></div>
<dl><dt><span class="strong">Returns:</span></dt><dd>a fresh copy of the coefficients array.</dd></dl>
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<h4>evaluate</h4>
<pre>public static&nbsp;double&nbsp;evaluate(double[]&nbsp;a,
              double[]&nbsp;c,
              double&nbsp;z)
                       throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
                              <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a>,
                              <a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></pre>
<div class="block">Evaluate the Newton polynomial using nested multiplication. It is
 also called <a href="http://mathworld.wolfram.com/HornersRule.html">
 Horner's Rule</a> and takes O(N) time.</div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - Coefficients in Newton form formula.</dd><dd><code>c</code> - Centers.</dd><dd><code>z</code> - Point at which the function value is to be computed.</dd>
<dt><span class="strong">Returns:</span></dt><dd>the function value.</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if any argument is <code>null</code>.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if any array has zero length.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the size difference between
 <code>a</code> and <code>c</code> is not equal to 1.</dd></dl>
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<h4>computeCoefficients</h4>
<pre>protected&nbsp;void&nbsp;computeCoefficients()</pre>
<div class="block">Calculate the normal polynomial coefficients given the Newton form.
 It also uses nested multiplication but takes O(N^2) time.</div>
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<h4>verifyInputArray</h4>
<pre>protected static&nbsp;void&nbsp;verifyInputArray(double[]&nbsp;a,
                    double[]&nbsp;c)
                                throws <a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a>,
                                       <a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a>,
                                       <a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></pre>
<div class="block">Verifies that the input arrays are valid.
 <p>
 The centers must be distinct for interpolation purposes, but not
 for general use. Thus it is not verified here.</p></div>
<dl><dt><span class="strong">Parameters:</span></dt><dd><code>a</code> - the coefficients in Newton form formula</dd><dd><code>c</code> - the centers</dd>
<dt><span class="strong">Throws:</span></dt>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NullArgumentException.html" title="class in org.apache.commons.math3.exception">NullArgumentException</a></code> - if any argument is <code>null</code>.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/NoDataException.html" title="class in org.apache.commons.math3.exception">NoDataException</a></code> - if any array has zero length.</dd>
<dd><code><a href="../../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</a></code> - if the size difference between
 <code>a</code> and <code>c</code> is not equal to 1.</dd><dt><span class="strong">See Also:</span></dt><dd><a href="../../../../../../org/apache/commons/math3/analysis/interpolation/DividedDifferenceInterpolator.html#computeDividedDifference(double[],%20double[])"><code>DividedDifferenceInterpolator.computeDividedDifference(double[],
 double[])</code></a></dd></dl>
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